kottke.org posts about sierpinskigasket

Infinite Jest once again proved finite, although it’s taken me since August to get through it. This book was such a revelation the first time through that I was afraid of a reread letdown but I enjoyed it even more this time around…and got much more out of the experience too.

MICHAEL SILVERBLATT: I don’t know how, exactly, to talk about this book, so I’m going to be reliant upon you to kind of guide me. But something came into my head that may be entirely imaginary, which seemed to be that the book was written in fractals.

DAVID FOSTER WALLACE: Expand on that.

MS: It occurred to me that the way in which the material is presented allows for a subject to be announced in a small form, then there seems to be a fan of subject matter, other subjects, and then it comes back in a second form containing the other subjects in small, and then comes back again as if what were being described were — and I don’t know this kind of science, but it just — I said to myself this must be fractals.

DFW: It’s — I’ve heard you were an acute reader. That’s one of the things, structurally, that’s going on. It’s actually structured like something called a Sierpinski Gasket, which is a very primitive kind of pyramidical fractal, although what was structured as a Sierpinski Gasket was the first- was the draft that I delivered to Michael in ‘94, and it went through some I think ‘mercy cuts’, so it’s probably kind of a lopsided Sierpinski Gasket now. But it’s interesting, that’s one of the structural ways that it’s supposed to kind of come together.

MS: “Michael” is Michael Pietsche, the editor at Little, Brown. What is a Sierpinski Gasket?

DFW: It would be almost im- … I would almost have to show you. It’s kind of a design that a man named Sierpinski I believe developed — it was quite a bit before the introduction of fractals and before any of the kind of technologies that fractals are a really useful metaphor for. But it looks basically like a pyramid on acid —

To answer Silverblatt’s question, a Sierpinski Gasket is constructed by taking a triangle, removing a triangle-shaped piece out of the middle, then doing the same for the remaining pieces, and so on and so forth, like so:

The result is an object of infinite boundary and zero area — almost literally everything and nothing at the same time. A Sierpinski Gasket is also self-similar…any smaller triangular portion is an exact replica of the whole gasket. You can see why Wallace would have wanted to structure his novel in this fashion.